Shape Solver Reference Sheet
Algebra Refreshes
Algebra Toolkit for Geometry Success
Desk Companion
STEP 0
Order of Operations (PEMDAS)
Simplify terms before you start solving equations!
P ( Parentheses )
E Exponents x²
M / D × and ÷ Left to Right
A / S + and - Left to Right
Example: Simplify 2(3 + 4) Do Parentheses first: 2(7) = 14
CONCEPT
What is a Variable?
x Unknown
It's just an empty box!
In geometry, x is simply a missing side length or dimension we need to find.
Example Rectangle Width = x, Height = 5 Area = 35
x 5 A = 35
THE CORE SKILL
Solving Equations: Step-by-Step
GOLDEN RULE: Keep it balanced! Do the exact same thing to both sides!
Inverse Operations
Opposite operations undo each other to isolate x.
Undo
-
×
Undo
÷
1 1-Step: Get x Alone
Apply a single opposite operation to solve.
Equation: 5x = 35
Undo Multiplied by 5: ÷ 5 both sides
5x / 5 = 35 / 5
x = 7
2 2-Step: Reverse Order
Always undo Addition/Subtraction FIRST!
Equation: 2x + 12 = 32
1. Undo + 12: - 12 both sides
2x = 20
2. Undo Multiply by 2: ÷ 2 both sides
x = 10
REAL MISSION
Putting it to Work in Geometry
Example A: Finding Missing Height (Area)
x 8 cm Area = 48 cm²
Formula: A = b · h
48 = 8 · x
÷ 8 both sides
x = 6 cm
Example B: Finding Missing Side (Perimeter)
x 12 in Perimeter = 34 in
Formula: P = 2l + 2w
34 = 2(x) + 2(12)
34 = 2x + 24
1. - 24 → 10 = 2x
2. ÷ 2 → x = 5 in
Check your answer: plug x back into the equation to see if it makes a true statement!
SHAPE SOLVER CHEAT SHEET
